<h2>题目编号 : 138</h2>
<div style="color:#666;font-size:80%;">20 January 2007</div><br />
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<p>Consider the isosceles triangle with base length, <i>b</i> = 16, and legs, L = 17.</p>
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<img src='project/images/p_138.gif' width='230' height='228' alt='' />
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<p>By using the Pythagorean theorem it can be seen that the height of the triangle, <i>h</i> = <img src='images/symbol_radic.gif' width='14' height='16' alt='&radic;' border='0' style='vertical-align:middle;' />(17<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> <img src='images/symbol_minus.gif' width='9' height='3' alt='&minus;' border='0' style='vertical-align:middle;' /> 8<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />) = 15, which is one less than the base length.</p>
<p>With <i>b</i> = 272 and L = 305, we get <i>h</i> = 273, which is one more than the base length, and this is the second smallest isosceles triangle with the property that <i>h</i> = <i>b</i> <img src='images/symbol_plusmn.gif' width='11' height='11' alt='&plusmn;' border='0' style='vertical-align:middle;' /> 1.</p>
<p>Find <img src='images/symbol_sum.gif' width='11' height='14' alt='&sum;' border='0' style='vertical-align:middle;' /> L for the twelve smallest isosceles triangles for which <i>h</i> = <i>b</i> <img src='images/symbol_plusmn.gif' width='11' height='11' alt='&plusmn;' border='0' style='vertical-align:middle;' /> 1 and <i>b</i>, L are positive integers.</p>

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